LONDON -- Human rights groups are concerned that Saudi Arabia has set a new legal precedent that could see women executed for peaceful activism. In an apparent first, Saudi prosecutors are seeking the death penalty against a female activist charged with non-violent offenses.

"Saudi Arabia has always had, sort of, red lines. There were certain things that they just didn't do," said Rothna Begum, a senior women's rights researcher at Human Rights Watch.

The fact that authorities are now seeking the death penalty in Israa al-Ghomgham's case suggests they "may want to do something very similar to the (other) women's rights activists," Begum said.

Women have been executed before in Saudi Arabia, which has one of the highest rates of execution in the world, notes Rachel Vogelstein, director of the Women and Foreign Policy Program at the Council on Foreign Relations, a think tank.

"The fact of execution in and of itself -- that's clearly not what is unique about this," Vogelstein told CBS News. "It is connecting the severity of this punishment to women's activism."

Samah Hadid, Amnesty International's Middle East director of campaigns, said in a statement last month that sentencing activist al-Ghomgham to death "would send a horrifying message that other activists could be targeted in the same way for their peaceful protest and human rights activism."

"The charges against Israa al-Ghomgam, which mostly relate to her peaceful participation in protests, are absurd and clearly politically motivated to silence dissent in the Eastern Province of Saudi Arabia," she said.

Al-Ghomgham is well known for both taking part in -- and documenting -- demonstrations in the province that started in early 2011, the year Arab Spring uprisings swept the region, says Human Rights Watch. Amnesty, citing court documents, says the charges against her are:

Violating Royal Decree 44/A for "participating in protests in al-Qatif and documenting these protests on social media"

"Providing moral support to rioters by participating in funerals of protesters killed during clashes with security forces"

"Violating Article 6 of the Anti-Cyber Crime law" by, among other things, posting videos and photos of protests on Facebook as well as advocating for protests

"Committing forgery by using the passport photo of another woman on her Facebook account"

Al-Ghomgham is facing the charges after several years during which the women's rights movement in Saudi Arabia has picked up steam. In wake of the Arab Spring protests, the field of activism, which had been dominated by men, started to see more female participants.

The government's response to the evolving role of women activists was initially limited.

"Before, (if a woman got in trouble with authorities for any sort of activism) they were only investigating or asking (the woman) to not do that activity again," Saudi activist Ali Adubisi told CBS News.

Adubisi, who now lives in Germany, gave an example of a time in 2011 when he and his wife were taken into custody in Saudi Arabia. She was quickly released, while he was placed under arrest. Adubisi said this wouldn't be the case today.

"Now the government wants to stop and shut down all the women's activity in Saudi Arabia," he said. "They want to send a strong message to women by arresting them for a long time and by giving them very harsh charges."

Just weeks before Saudi Arabia lifted the world's only ban on women driving in June, the government launched what HRW has called an "unprecedented" crackdown on the women's rights movement. More than a dozen women's rights activists were arrested and several were accused of "grave crimes" that appear to be linked to their activism, the organization said.

The crackdown has come as women in the country have gained some freedoms. In addition to the repeal of the female driving ban, women can now apply to serve in the military and attend sports events at public stadiums.

"We're seeing these changes, they're significant changes, and yet the message the government is sending is that further reform and activism will be met with severe crackdowns," said Vogelstein at the Council on Foreign Relations.

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In addition to al-Ghomgham, four other Eastern Province activists are facing a possible death sentence, says Human Rights Watch. They are being tried in a counter-terror court. October 28 is their next scheduled court date.

They are "facing the most appalling possible punishment simply for their involvement in anti-government protests," said Amnesty's Hadid. "We are urging the Saudi Arabian authorities to drop these plans immediately."